Spectral instability of charged scalar quasinormal modes and superradiance: Stabilizing the unstable

Abstract

The spectral instability of black holes has become a central topic of the black-hole spectroscopy program. Small changes to the black-hole scattering potential are known to produce disproportionately large migrations of its quasinormal modes in the complex plane, but it is unclear whether this sensitivity carries over to energy extraction through superradiance. We study this relation for massless charged scalar fields on Reissner--Nordström and Reissner--Nordström--de Sitter backgrounds. A localized positive potential bump, small in mass-scaled height, is displaced outward from the light ring while the original radiative boundary conditions are preserved. In the asymptotically flat case, a quasinormal branch enters the superradiant frequency regime while remaining damped. By searching for competing modes, we show that the least-damped positive-frequency mode also enters this regime, after a series of mode overtakings driven by quasinormal-mode migration. The real-frequency amplification, nevertheless, is only weakly affected and develops no pronounced narrow resonance. In de Sitter black holes, the bump can move an initially growing monopole mode into the damped half of the complex plane, stabilizing selected configurations that are initially modally unstable. After stabilization, the peak superradiant amplification can remain above both its unperturbed value and a gain of $100\%$; it falls below $100\%$ only for more distant bump locations. A prescribed positive perturbation can thus suppress modal growth without changing the superradiant frequency bounds or immediately suppressing the scattering peak.